Category: Integration

Question Number 115367 by Bird last updated on 25/Sep/20 $${solve}\:{xy}^{''} −\left({x}^{\mathrm{2}} +\mathrm{1}\right){y}^{'} \:\:={x}^{\mathrm{2}} {sin}\left(\mathrm{2}{x}\right) \\ $$ Answered by Olaf last updated on 26/Sep/20 $$ \\…

Question Number 115364 by Bird last updated on 25/Sep/20 $${calculate}\:\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{2}} } \:\:\sqrt{{xy}}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right){dxdy} \\ $$ Answered by Olaf last updated on 25/Sep/20 $$\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{2}} }…

Question Number 49827 by rahul 19 last updated on 11/Dec/18 $${The}\:{integral}\:\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \frac{\mathrm{ln}\:\left(\mathrm{1}+\mathrm{2}{x}\right)}{\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}} }{dx}\:=\:? \\ $$$$\left.{a}\left.\right)\left.\:\left.\frac{\pi}{\mathrm{4}}{ln}\mathrm{2}\:\:\:\:{b}\right)\frac{\pi}{\mathrm{8}}{ln}\mathrm{2}\:\:\:\:{c}\right)\frac{\pi}{\mathrm{16}}{ln}\mathrm{2}\:\:\:{d}\right)\frac{\pi}{\mathrm{32}}{ln}\mathrm{2} \\ $$ Commented by rahul 19 last updated on…

Question Number 115361 by Bird last updated on 25/Sep/20 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left(\pi{x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{2}} }{dx} \\ $$ Answered by Olaf last updated on 27/Sep/20 $$\frac{\pi\left[\mathrm{6}\pi\left(\boldsymbol{\mathrm{C}}\left(\sqrt{\mathrm{6}}\right)−\boldsymbol{\mathrm{S}}\left(\sqrt{\mathrm{6}}\right)\right)+\boldsymbol{\mathrm{C}}\left(\sqrt{\mathrm{6}}\right)−\boldsymbol{\mathrm{S}}\left(\sqrt{\mathrm{6}}\right)+\sqrt{\mathrm{6}}−\mathrm{1}\right]}{\mathrm{12}\sqrt{\mathrm{3}}}…

Question Number 49815 by Aditya789 last updated on 11/Dec/18 $$\mathrm{sin}^{\mathrm{6}} \mathrm{x}−\mathrm{cos}^{\mathrm{6}} \mathrm{x}/\mathrm{sin}^{\mathrm{2}} \mathrm{xcos}^{\mathrm{2}} \mathrm{x} \\ $$ Commented by Abdo msup. last updated on 12/Dec/18 $${if}\:{you}\:{mean}\:{simification}…